DIP: Graphical Model Construction by System Decomposition: Increasing the Utility of Algebra Story Problem Solving

网络学习和未来学习技术计划资助的努力将有助于展望下一代学习技术，并促进我们对人们在技术丰富的环境中如何学习的了解。这个项目研究了一种新的学习技术，它可能会消除STEM教育中一个臭名昭著的瓶颈：数学模型构建。如今，计算机可以解决复杂的数学问题，但人类仍然必须为计算机定义问题，这称为构建系统模型。许多学生可以学习程序技能，例如求解二次方程，但构建模型会让他们感到沮丧，因为没有程序。这有效地阻止了他们在数学方面的进步，并阻止了他们进入STEM专业。这可能就是为什么模型构建是同时出现在数学(CCSSM)和科学(NGSS)标准中的少数实践之一。解决这些问题的关键创新是一种基于两种思想的新型学习技术。首先，它强调将给定的系统描述分解为多个子系统。其次，虽然最终的模型是一组代数方程，但该模型首先被构建为一个节点-链接图，该图显示了哪些量与哪些关系有关。使用贝叶斯知识追踪的隐形评估将允许对学生提交的模型进行反馈，以响应建模中的文字问题。当模型表示为TopOMath图时，通常可以将其绘制为不同的子系统对应于不同的子图。这使学生更容易理解模型和所代表的系统之间的关系。此外，当通过将系统分解为多个子系统来构建模型时，TopOMath图中的空白区域会提示哪些子系统仍然需要建模。这些只是将系统分解和TopOMath的数学模型的图形表示相结合的协同效应的一小部分。这个项目将探索拓扑数学学习活动的顺序，目的是让学生在20个小时的教学中掌握模型构造。该教学将在相当于高中代数2班的大学数学补习班的背景下进行。教学内容包括使用拓扑数学技术的个人、小组和全班活动。将使用知识-学习-指导框架对口头协议进行定性分析，以进行系统评估，并更好地理解由系统的表征和建模支架支持的模型构建中的学习过程。

The Cyberlearning and Future Learning Technologies Program funds efforts that will help envision the next generation of learning technologies and advance what we know about how people learn in technology-rich environments. Development and Implementation (DIP) Projects build on proof-of-concept work that shows the possibilities of the proposed new type of learning technology, and PI teams build and refine a minimally-viable example of their proposed innovation that allows them to understand how such technology should be designed and used in the future and that allows them to answer questions about how people learn, how to foster or assess learning, and/or how to design for learning. This project studies a new genre of learning technology that may remove a notorious bottleneck in STEM education: mathematical model construction. These days, computers can solve complex mathematical problems, but humans must still define the problem for the computer, which is called constructing a model of a system. Many students can learn procedural skills, such as solving a quadratic equation, but constructing a model frustrates them because there is no procedure. This effectively stops their progress in math and blocks their entry to STEM professions. That may be why model construction is one of the few practices that appears in both math (CCSSM) and science (NGSS) standards. The key innovation for solving these problems is a new genre of learning technology based on two ideas. First, it emphasizes decomposing the given system description into subsystems. Second, although the final model is a set of algebraic equations, the model is first constructed as a node-link graph that shows which quantities are connected to which relationships. This notation is called TopoMath.TopoMath builds on prior success with the Dragoon intelligent tutoring system, and represents a revision of that system to support a novel graphical representation to allow learners to recognize distinct problem-solving schemata. Stealth assessment using Bayesian Knowledge Tracing will allow feedback on student submitted models in response to word problems in modelling. When a model is represented as a TopoMath graph, it can usually be drawn such that distinct subsystems correspond to distinct subgraphs. This makes it easier for students to understand the relationship between the model and the system that is represents. Moreover, when constructing a model by decomposing a system into subsystems, blank areas in the TopoMath graph suggest which subsystems still need to be modeled. Students can learn model construction schemas by comparing and generalizing systems that have visually similar TopoMath models so that when constructing a model by decomposing a system into subsystems, if a schema matches a subsystem, then a whole section of the model can be filled in without further decomposition. These are just a few of the synergies of combining system decomposition and TopoMath's graphical representation of mathematical models. This project will explore sequences of TopoMath learning activities with the goal of bringing students to model construction mastery with just 20 hours of instruction. The instruction will be developed in the context of remedial college math classes that are equivalent to high school algebra 2 classes. The instruction will include individual, small group and whole class activities using the TopoMath technology. Qualitative analysis of verbal protocols will be undertaken using the Knowledge-Learning-Instruction framework both for system evaluation, and to better understand the processes of learning in model construction that are supported by the system's representations and scaffolds for modeling.